Mathematical modelling of unsteady solute dispersion in two-fluid (micropolar-Newtonian) blood flow with bulk reaction

Roy, AK; Beg, OA

Abstract

A mathematical model is developed for axisymmetric, incompressible, and fully
developed hemodynamic transport of a reactive diffusing species, e. g. oxygen, in a rigid,
impermeable artery under constant axial pressure gradient which undergoes a first-order
chemical reaction with streaming blood. A two-fluid model is deployed where the core region is
simulated as an Eringen micropolar fluid, and the plasma layer engulfing the core, i.e., near the
boundary, is analyzed as a Newtonian viscous fluid. At the interface of the core and plasma
region, the velocity and shear stress are equal, and micro-rotation is constant. Closed-form
solutions are presented for the velocity and micro-rotation profiles, and a Gill decomposition
method is deployed for the concentration field. Expressions are derived for the dispersion
coefficient, mean and transverse concentration functions. Transverse concentration is observed
to be enhanced with increasing micropolar coupling number (N) and reaction rate ( );
however, it is reduced with greater micropolar material parameter (s) and viscosity ratio ( ).
Additionally, graphs are presented for the evolution in dispersion coefficient, and the rate of
dispersion coefficient with micropolar parameters is examined. Finally, both axial and transverse
mean concentration distributions for all key parameters are investigated. Transverse
concentration is observed to be enhanced with increasing micropolar coupling number and
reaction rate; however, it is reduced with greater micropolar material parameter and viscosity
ratio. Axial mean concentration peaks are reduced in magnitude and displaced further along the
arterial geometry with greater micropolar material parameter values, whereas the opposite effect
is induced with greater micropolar coupling number. A slight increase in axial mean
concentration peak value is computed with increasing reaction parameter. The dispersion
coefficient is reduced with increasing micropolar material parameter but grows with a greater
viscosity ratio. The study is relevant to hemorheology, diseased arteries and coagulating
hemodynamics and may help physiologists and clinicians in furnishing a more refined
understanding of diffusion processes in cardiovascular hydrodynamics.

Citation

Roy, A., & Beg, O. (2021). Mathematical modelling of unsteady solute dispersion in two-fluid (micropolar-Newtonian) blood flow with bulk reaction. International Communications in Heat and Mass Transfer, 122, 105169. https://doi.org/10.1016/j.icheatmasstransfer.2021.105169

• Journal Article Type: Article
• Acceptance Date: Jan 25, 2021
• Online Publication Date: Feb 9, 2021
• Publication Date: Mar 1, 2021
• Deposit Date: Jan 26, 2021
• Publicly Available Date: Feb 9, 2022
• Journal: International Communications in Heat and Mass Transfer
• Print ISSN: 0735-1933
• Publisher: Elsevier
• Volume: 122
• Pages: 105169
• DOI: https://doi.org/10.1016/j.icheatmasstransfer.2021.105169
• Publisher URL: https://doi.org/10.1016/j.icheatmasstransfer.2021.105169
• Related Public URLs: http://www.journals.elsevier.com/international-communications-in-heat-and-mass-transfer/